用贝叶斯模型分析工程课学生答题数据，精准识别难点与学习差异。
Hierarchical Bayesian Knowledge Tracing in Undergraduate Engineering Education
- 基于分层贝叶斯建模，同时估计知识点难度与学生个体能力。
- 发现部分概念普遍难掌握，另一些则易学会，存在明显学习轨迹分组。
- 结果直观可解释，适合教育者做个性化教学决策。
教授入门级大学工程课程的教师面临识别学生最困难知识点及有效支持多样化学习需求的挑战。本研究展示了一种严谨且可解释的统计方法——分层贝叶斯建模，利用大规模学生作答数据，量化知识点难度与个体学生能力。基于某本科静力学课程的大规模数据集，我们识别出清晰的技能掌握模式，并根据学习轨迹发现不同的学生子群体。分析表明，某些概念始终难以掌握，需针对性教学支持；而另一些概念则易于掌握，可开展拓展活动。重要的是，分层贝叶斯方法为教育者提供了直观可靠的指标，既保持预测准确性，又提升可解释性。该方法支持数据驱动的教学决策，推动个性化教学策略，提升学生参与度与学业成功率。通过结合强统计性能与高可解释性，本研究为教育者提供了可操作的洞察，以更好支持多样化学习者群体。
原文摘要 · Abstract (English)
Educators teaching entry-level university engineering modules face the challenge of identifying which topics students find most difficult and how to support diverse student needs effectively. This study demonstrates a rigorous yet interpretable statistical approach -- hierarchical Bayesian modeling -- that leverages detailed student response data to quantify both skill difficulty and individual student abilities. Using a large-scale dataset from an undergraduate Statics course, we identified clear patterns of skill mastery and uncovered distinct student subgroups based on their learning trajectories. Our analysis reveals that certain concepts consistently present challenges, requiring targeted instructional support, while others are readily mastered and may benefit from enrichment activities. Importantly, the hierarchical Bayesian method provides educators with intuitive, reliable metrics without sacrificing predictive accuracy. This approach allows for data-informed decisions, enabling personalized teaching strategies to improve student engagement and success. By combining robust statistical methods with clear interpretability, this study equips educators with actionable insights to better support diverse learner populations.
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